a1 Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia (email: email@example.com)
The main objective of this paper is a study of some new refinements and converses of multidimensional Hilbert-type inequalities with nonconjugate exponents. Such extensions are deduced with the help of some remarkable improvements of the well-known Hölder inequality. First, we obtain refinements and converses of the general multidimensional Hilbert-type inequality in both quotient and difference form. We then apply the results to homogeneous kernels with negative degree of homogeneity. Finally, we consider some particular settings with homogeneous kernels and weighted functions, and compare our results with those in the literature.
(Received June 03 2011)
2010 Mathematics subject classification
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This research was supported by the Croatian Ministry of Science, Education, and Sports, under Research Grant 036–1170889–1054.